For compote, stir together the grape juice, honey, and ginger in a small saucepan. Bring to boiling; remove from heat. Cool for 1 hour. Place melon balls in a medium bowl; pour juice mixture over melon. Cover and chill for 8 hours or overnight, gently stirring occasionally.

For baskets, preheat oven to 350 degrees F. Line a cookie sheet with foil. Grease the foil; set aside. Stir together the brown sugar, butter or margarine, and corn syrup in a medium bowl. Stir in almonds and flour until combined. Drop batter by tablespoonfuls onto prepared cookie sheet, baking only 2 or 3 at a time. Spread each to about 3 inches in diameter. (You should end up with 8 portions.) Bake in the preheated oven for 6 to 8 minutes or until bubbly and deep golden brown. Let stand 1 to 2 minutes or until set but still pliable. Quickly shape into baskets by placing each inside a 6-ounce custard cup. Cool completely in cups. (Do not bake more shells at a time than you have custard cups for them.)

To serve, fill almond baskets with melon mixture using a slotted spoon. Top each with a small scoop of frozen yogurt. If desired, garnish with mint. Serve immediately. Make 8 servings.

Prepare the cookie baskets up to 1 week ahead and store in an airtight container.